There is broad international agreement about the importance of increasing participation in science once it is no longer compulsory in school, particularly among groups who have been historically underrepresented in science. Previous research reflects that despite broadly positive attitudes to science in and outside of school, there is limited translation of these attitudes into later aspirations and participation in science. The ASPIRES project, a five-year longitudinal study, has sought to understand students' science and career aspirations between the ages of 10 and 14 and to identify factors that contribute to, or hinder, the development of aspirations in science. Utilising data from two cross-sectional surveys conducted with students in their last year of primary school (9300 students) and in their third year of secondary school (4,600 students), we explore who is most likely to hold science aspirations and what factors seem to be connected to those aspirations at both time points. Descriptive, multivariate and multilevel modelling analyses of the data reflect consistency in who holds science aspirations, as well as highlighting that the factors connected to these aspirations--attitudes to school science and parental attitudes--are similar at both times. However, for many students, positive attitudes to school science and positive parental attitudes to science are not translating into children wanting a career in science. We suggest that differences in "science capital" may help explain this persistent gap.